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portada Zero-Divisor Graphs of Some Algebraic Structures
Type
Physical Book
Publisher
Author
Language
English
Pages
184
Format
Paperback
Dimensions
22.9x15.2x1.1 cm
ISBN13
9786209231346

Zero-Divisor Graphs of Some Algebraic Structures

Patil, Avinash (Author) · LAP Lambert Academic Publishing · Paperback

Zero-Divisor Graphs of Some Algebraic Structures - Patil, Avinash

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Synopsis "Zero-Divisor Graphs of Some Algebraic Structures"

This book studies a graph assigned to the zero divisors of a ring with involution *, which is an anti-homomorphism of order two. The *-rings with zero-divisor graph connected are characterized and results about chromatic number, clique number, girth are obtained. An equivalent condition for adjacency in the zero-divisor graph of Rickart *-rings is obtained using the right projections. The zero-divisors graphs of Rickart *-rings are thoroughly investigated using the prime strict spectrum. Also, the zero-divisor graphs of dismantlable lattices are examined and are used to obtain the zero-divisor graphs of Rickart *-rings. The zero-divisor graphs of dismantlable lattices are characterized using the comparability graphs and non-ancestor graphs. For two lower dismantlable lattices, it is proved that their zero-divisor graphs are isomorphic if and only if the lattices are isomorphic. At last, the orthogonality graphs of ortho lattices are investigated and their connection with zero-divisor graphs is established.

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